Is it possible to turn off sorting questions by popularity so that the most recent ones appear first? ?

At the top of the list click "Answer" instead of "Discover".

Most recent questions show up first by default.

That's the way they show up (most recently posted first), at least on desktop computers. Make sure you're clicked on the Answer tab, not the Discover tab. Whether it's the main 'all categories' YA page or any category/subcategory, the question list is in chronological order, with the most recently posted at the top of the list. You can customize the question lists (feed) to show ones with No Best Answer but that's the only way you can reorganize the list (again, on a desktop). If mobile devices are set up differently any filtering options (if available) should be at the top of the question list.

No there is not you do not have any Control over what Questions show up first